Grammatical Evolution

Grammatical Evolution #

Name #

Grammatical Evolution (GE)

Taxonomy #

Grammatical Evolution is an evolutionary algorithm that evolves computer programs or rules using a technique called grammar-guided genetic programming. It is closely related to Genetic Programming (GP) and Genetic Algorithms (GA).

  • Computational Intelligence
    • Biologically Inspired Computation
      • Evolutionary Computation
        • Genetic Programming
          • Grammatical Evolution

Strategy #

Grammatical Evolution is a population-based optimization algorithm that uses a context-free grammar to guide the generation and evolution of solutions. The grammar is typically specified in Backus-Naur Form (BNF) and defines the structure and syntax of the solutions that can be evolved.

Genotype Representation #

In GE, solutions are represented as variable-length integer arrays called genotypes. Each integer in the genotype corresponds to a production rule in the grammar. The genotype is used to select production rules from the grammar during the mapping process.

Genotype-to-Phenotype Mapping #

The genotype-to-phenotype mapping process converts the integer genotype into a valid solution (phenotype) according to the rules defined in the grammar. The mapping starts with the start symbol of the grammar and recursively applies production rules based on the integer values in the genotype until a complete solution is generated.

Evolutionary Process #

GE follows the standard evolutionary process of selection, crossover, and mutation. The fitness of each solution is evaluated based on a predefined fitness function. Parents are selected for reproduction based on their fitness, and offspring are created through crossover and mutation operations applied to the genotypes.

Wrapping and Invalid Solutions #

If the end of the genotype is reached during the mapping process without generating a complete solution, a wrapping mechanism is used to reuse the genotype integers from the beginning. If the mapping process results in an invalid solution that violates the grammar rules, the solution is assigned a low fitness value to discourage its selection in future generations.

Procedure #

  1. Initialize the population
    1. Generate a population of random integer genotypes
    2. Map each genotype to its corresponding phenotype using the grammar
    3. Evaluate the fitness of each individual in the population
  2. While termination condition is not met, repeat:
    1. Select parents for reproduction based on their fitness
    2. Create offspring through crossover and mutation operations on the genotypes
      1. Apply crossover to the selected parents to generate offspring genotypes
      2. Apply mutation to the offspring genotypes
    3. Map the offspring genotypes to their corresponding phenotypes using the grammar
    4. Evaluate the fitness of the offspring
    5. Select individuals for the next generation based on fitness (e.g., replace worst individuals with offspring)
  3. Return the best solution found

Data Structures #

  • Genotype: An integer array representing the solution in the search space
  • Phenotype: The actual solution generated by mapping the genotype using the grammar
  • Grammar: A context-free grammar defining the structure and syntax of valid solutions
  • Population: A collection of individuals (genotypes and their corresponding phenotypes)

Parameters #

  • Population Size: The number of individuals in the population
  • Max Generations: The maximum number of generations to run the algorithm
  • Crossover Probability: The probability of applying crossover to selected parents
  • Mutation Probability: The probability of applying mutation to offspring genotypes
  • Wrapping Count: The maximum number of times the genotype can be wrapped during mapping

Considerations #

Advantages #

  • Ability to evolve solutions with complex structures and constraints defined by the grammar
  • Separation of search space (genotype) and solution space (phenotype) allows for flexible representation
  • Suitable for problems where the optimal solution structure is not known in advance

Disadvantages #

  • Designing an appropriate grammar for the problem domain can be challenging and time-consuming
  • Mapping process can be computationally expensive, especially for large grammars and genotypes
  • Redundancy in the genotype representation can lead to inefficiencies in the search process

Heuristics #

Grammar Design #

  • Use a modular and hierarchical grammar structure to facilitate the evolution of meaningful solutions
  • Ensure that the grammar covers the necessary solution space while avoiding unnecessary complexity
  • Consider incorporating domain knowledge into the grammar to guide the search process effectively

Population Initialization #

  • Generate a diverse initial population to explore different regions of the search space
  • Ensure that the initial genotypes have sufficient length to generate valid phenotypes

Selection and Reproduction #

  • Use selection methods that balance exploration and exploitation, such as tournament selection or rank-based selection
  • Adjust the crossover and mutation probabilities based on the problem complexity and desired level of exploration

Wrapping and Invalid Solutions #

  • Set an appropriate wrapping count to strike a balance between allowing the reuse of genotype information and preventing excessive wrapping that may lead to inefficiencies
  • Consider implementing repair mechanisms or penalty functions to handle invalid solutions and guide the search towards valid regions of the search space

Parameter Tuning #

  • Experiment with different parameter settings to find the optimal configuration for the specific problem
  • Use parameter control techniques, such as adaptive or self-adaptive parameters, to dynamically adjust the parameters during the evolutionary process

Hybridization #

  • Consider hybridizing Grammatical Evolution with other optimization techniques, such as local search or machine learning, to improve the search efficiency and solution quality
  • Incorporate domain-specific heuristics or knowledge into the evolutionary process to guide the search towards promising regions of the search space